The present invention relates generally to workpiece shape control in a rolling mill and more particularly to the control of workpiece shape through control of workpiece crown.
Workpiece crown is used here in its usual sense to denote the difference in thickness between the center and the edges of a workpiece. When the center is thicker than the edges, the workpiece is said to have positive crown while if the workpiece is thinner in the center than at the edges it is said to have negative crown. Positive crown is by far the more common occurrence. One aspect of workpiece shape control is workpiece flatness; that is, the workpiece does not exhibit centerline buckle nor wavy edges. Centerline buckle is normally occasioned by a greater elongation at the workpiece center than at the edges such that the resultant increased elongation shows up in a buckle in the center of the workpiece whereas wavy edges are occasioned by a greater elongation at the edges of the workpiece than at the center. Thus, by controlling the workpiece crown, the relative reductions of the center and the edges, and hence the flatness, are controlled.
For a more complete description of the various reasons for having crown in a workpiece and for a description of a system in which crown control is used to control workpiece shape, reference is made to U.S. Pat. No. 3,630,055, "Workpiece Shape Control" by D. J. Fapiano et al, issued Dec. 28, 1971 and assigned to the assignee of the present invention. This patent is specifically incorporated hereinto by reference and describes and claims a method to which the present invention is an improvement. The U.S. Pat. No. 3,630,055 describes a system for workpiece shape control which is subject to automation and which recognizes that the workpiece crown is a function of mill and workpiece dimensions, rolling force, and workpiece resistant to deformation. That patent also recognizes that workpiece flatness is not totally dependent upon the crown but can be modified independently of the final plate crown by altering the per unit workpiece crown on successive passes. This latter feature was accomplished through the use of what is there described and identified as a "crown slope multiplier" (CSM). The CSM is a factor having a magnitude greater than unity and represents the relative deformation a workpiece may experience without exhibiting wavy edges or center buckle. This factor of CSM results largely from the ability of the material to withstand interboundary stresses and normally increases with the material thickness but is also affected by parameters such as material composition and temperature. The actual values of CSM are usually empirically derived for the materials being rolled as a function of the various parameters.
The system of the U.S. Pat. No. 3,630,055 patent exercised control to establish a particular crown during each pass by determining the roll separating force necessary to produce that crown in accordance with the equation: EQU F = (RM) (RD) [(MH) (PCW) (TC) + (RCW) (ERC)].
in this equation and in accordance with that patent, RM is proportional to the modulus of elasticity of the rolls, RD is proportional to the diameter of the rolls, MH is proportional to the resistance to deformation of the workpiece, PCW and RCW are proportional to the width of the plate, TC is proportional to the target crown on the workpiece, and ERC is proportional to the effective crown on the rolls.
The method represented by and employing the above formula is entirely satisfactory for the majority of metal hot rolling requirements. It has been more recently determined, however, that in certain instances the results achieved by the use of the method set forth in the patent are not, in all cases, as accurate as might be desired. This is particularly true when the workpiece is being rolled at lower than normal temperatures, for improved physical characteristics, or when the delivered workpiece is very thin. The basic deficiency which has been found to exist at these times is primarily the result of the fact that the prior art method as specified above assumes negligible correlation between entry and delivery workpiece crowns. In addition, this prior art method does not accommodate negative workpiece crowns and severely restricts allowed crown changes in the case of very low final workpiece crowns. This latter restriction can create difficulties in some present day rolling practices in which the final finishing roll force is specified by the mill operator rather than by the control system. Should the specified force result in a zero or negative finished workpiece crown, the system of the prior art just described would not operate properly. This condition, of course, does not arise when finishing force is designated by the control system, but this optional operating mode is sometimes valuable.